I. Ya. Aref'eva, N. V. Bulatov, S. Yu. Vernov, “Stable exact solutions in cosmological models with two scalar fields”, TMF, 163:3 (2010), 475–494; Theoret. and Math. Phys., 163:3 (2010), 788

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 163, Number 3, Pages 475–494
DOI: https://doi.org/10.4213/tmf6516 (Mi tmf6516)

This article is cited in 45 scientific papers (total in 45 papers)

Stable exact solutions in cosmological models with two scalar fields

I. Ya. Aref'eva^a, N. V. Bulatov^b, S. Yu. Vernov^c

^a Steklov Mathematical Institute, RAS, Moscow, Russia
^b Lomonosov Moscow State University, Moscow, Russia
^c Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

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DOI: https://doi.org/10.4213/tmf6516

Abstract: We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann–Robertson–Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field theory.

Keywords: cosmology, stability, Bianchi metric.

English version:
Theoretical and Mathematical Physics, 2010, Volume 163, Issue 3, Pages 788–803
DOI: https://doi.org/10.1007/s11232-010-0063-x

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: I. Ya. Aref'eva, N. V. Bulatov, S. Yu. Vernov, “Stable exact solutions in cosmological models with two scalar fields”, TMF, 163:3 (2010), 475–494; Theoret. and Math. Phys., 163:3 (2010), 788–803

Citation in format AMSBIB

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https://doi.org/10.4213/tmf6516

https://www.mathnet.ru/eng/tmf/v163/i3/p475

This publication is cited in the following 45 articles:

Prasanta Sahoo, Nandan Roy, Himadri Shekhar Mondal, “Quintessence scalar field and cosmological constant: dynamics of a multi-component dark energy model”, Gen Relativ Gravit, 57:2 (2025)
Vsevolod R. Ivanov, Sergey Yu. Vernov, “New integrable chiral cosmological models with two scalar fields”, Phys. Rev. D, 110:10 (2024)
V. R. Ivanov, S. Yu. Vernov, “Anisotropic Solutions for $\boldsymbol{R^{2}}$ Gravity Model with a Scalar Field”, Phys. Atom. Nuclei, 86:6 (2023), 1526
Bayron Micolta-Riascos, Alfredo D. Millano, Genly Leon, Cristián Erices, Andronikos Paliathanasis, “Revisiting Fractional Cosmology”, Fractal Fract, 7:2 (2023), 149 $https://doi.org/10.3390/fractalfract7020149$
Sergey Vernov, Vsevolod Ivanov, The 2nd Electronic Conference on Universe, 2023, 17
Jorge G. Russo, “New exact solutions in multi-scalar field cosmology”, J. Cosmol. Astropart. Phys., 2023:07 (2023), 066
Genly Leon, Saikat Chakraborty, Sayantan Ghosh, Raja Solanki, P.K. Sahoo, Esteban González, “Scalar Field Evolution at Background and Perturbation Levels for a Broad Class of Potentials”, Fortschritte der Physik, 71:10-11 (2023)
Do T.Q., Kao W.F., “Anisotropic Hyperbolic Inflation For a Model of Two Scalar and Two Vector Fields”, Eur. Phys. J. C, 82:2 (2022), 123
Ivanov V.R. Vernov S.Yu., “Integrable Cosmological Models With An Additional Scalar Field”, Eur. Phys. J. C, 81:11 (2021), 985
Kumar K.S., Maheshwari Sh., Mazumdar A., Peng J., “An Anisotropic Bouncing Universe in Non-Local Gravity”, J. Cosmol. Astropart. Phys., 2021, no. 7, 025
Do T.Q., Kao W.F., “Anisotropic Power-Law Inflation For a Model of Two Scalar and Two Vector Fields”, Eur. Phys. J. C, 81:6 (2021), 525
Christodoulidis P., “General Solutions to N-Field Cosmology With Exponential Potentials”, Eur. Phys. J. C, 81:5 (2021), 471
Vernov S.Yu. Ivanov V.R. Pozdeeva E.O., “Superpotential Method For F(R) Cosmological Models”, Phys. Part. Nuclei, 51:4 (2020), 744–749
Zubair M. Kousar F. Waheed S., “Dynamics of Scalar Potentials in F(R, R Alpha Beta R Alpha Beta, Phi) Theory of Gravity”, Can. J. Phys., 97:8 (2019), 880–894
Dimakis N. Paliathanasis A. Terzis P.A. Christodoulakis T., “Cosmological Solutions in Multiscalar Field Theory”, Eur. Phys. J. C, 79:7 (2019), 618
Paliathanasis A. Leon G. Pan S., “Exact Solutions in Chiral Cosmology”, Gen. Relativ. Gravit., 51:9 (2019), 106
Chervon S.V. Fomin I.V. Pozdeeva E.O. Sami M. Vernov S.Yu., “Superpotential Method For Chiral Cosmological Models Connected With Modified Gravity”, Phys. Rev. D, 100:6 (2019), 063522
Leon G., Paliathanasis A., “Extended Phase-Space Analysis of the Horava-Lifshitz Cosmology”, Eur. Phys. J. C, 79:9 (2019), 746
H. Hossienkhani, V. Fayaz, S. A. A. Terohid, N. Azimi, Z. Zarei, M. Ganji, “Anisotropic cosmology with a dilaton field coupled to ghost dark energy”, Theoret. and Math. Phys., 194:3 (2018), 415–438
Pozdeeva E.O. Vernov S.Yu., “Induced Gravity Models With Exact Bounce Solutions”, Phys. Part. Nuclei, 49:5 (2018), 914–917

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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